I am a compulsive problem solver, and always on hunt for new problems that make me sweat my brains. Here are some of the problems that I enjoyed solving during the wee hours of many nights. I will keep on updating problems in this article. Although the level of geomtery required in MBA exams is lower than that of the problems covered here, I have experienced that solving problems like these tests the fundamentals and strengthen the ability to apply all the fundamentals at the same time. Next week I am going to pose a challenger here, a problem that will test all your geometry fundamentals in one go. Till then, enjoy these!- Total Gadha

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the questions were good but i would want that you plz provide some lessons on topics where a cone is insribed in a cylinder of minimum volume and we r required to find radius or height, or where sphere is inscribed in cone of mininum volume and we have to find its height and similar types.....

1. Considering it a equilateral triangle and assuming n = 2 , we have MN=x, and QR = 2x with M,N as mid points of PQ and PR respectively and S as the Centroid.Let us take a point O on QR s.t. PO is perpendicular to QR. so PO is the height = H , PS = 2H/3 , SO = H/3

Now triangles MNS and RQS are similar , so height of triangle MNS : height of triangle RQS = 2

Hello sir,in q-2 cant we solved by this way...If we extend cb and aq and make another triangle let say acd...as cp:pq = 2:1 then it should be the median of new triangle..and angle cqa =90 so its also altitude..so the acd is equilitral? or ..so angle C=60?? pl suggest..

Yes there is mathematical proof for the same. This is calculated by area under the curve method in calculus.

The cone can be considered as a stack of no. of circular strips. which upon integration form 0 to h gives 1/3 (pi) R*R h

Suppose we want to find the volume of a circular cone of base radius r and height h, we slice the cone into an infinite number of circular discs of thickness dx (imagin) and find the volumes of all these discs and add them up. Consider the origin as the pointed end of the cone and the axis through the center of each cross section perpendicular to the base as the x-axis. Consider a line through the origin perpendicular to the x-axis as the y-axis. Consider a circular disc of thickness dx at a distance x from origin. Let y be the radius of this disc. We know that volume of this disc = pi.y.y.dx where pi = 3.14 nearly. As integration is summation the volume of the cone = integral of pi.y.y.dx for x limits 0 to h. We know y/x = tan a where a is the angle of the cone. Also r/h = tan a. So y = (r/h)x. Substituting this value of y in terms of x and integrating between the limits 0 to h we get the volume of the cone as (1/3)pi.r.r.h (one third pi r squared h).

This is my first post.I have problem in finding the optimized volume/curved surface area of a cylinder inscribed in a cone of radius r and height h. When similar thing is done in a semi sphere we take half of the semi sphere and find the optimized square that can be taken inside this part. Please help!!